Extending Fundamental Formulas From Classical B-Splines To Quantum B-Splines
| Autor: | Çetin Dişibüyük, Halil Oruç, Gülter Budakçı, Ron Goldman |
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| Rok vydání: | 2015 |
| Předmět: |
Quantum geometry
Pure mathematics Quantum t-design Applied Mathematics Mathematical analysis Convolution of probability distributions Mathematics::Numerical Analysis Computational Mathematics Computer Science::Graphics Quantum operation Quantum algorithm Divided differences Quantum statistical mechanics Quantum Mathematics |
| Popis: | We derive a collection of fundamental formulas for quantum B-splines analogous to known fundamental formulas for classical B-splines. Starting from known recursive formulas for evaluation and quantum differentiation along with quantum analogues of the Marsden identity, we derive quantum analogues of the de Boor Fix formula for the dual functionals, explicit formulas for the quantum B-splines in terms of divided differences of truncated power functions, formulas for computing divided differences of arbitrary functions by quantum integrating certain quantum derivatives of these functions with respect to the quantum B-splines, closed formulas for the quantum integral of the quantum B-splines over their support, and finally a 1/q-convolution formula for uniform g-B-splines. (C) 2015 Elsevier B.V. All rights reserved. |
| Databáze: | OpenAIRE |
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